Constructions using Geometer's Sketchpad

Before We Start.

  • Go to the Display Menu. Choose Preferences.

    Check the box Next to AutoShow Labels for Points.

    Make sure you are using degrees to measure the angles.

    Set the Precisions to Hundreths.

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    Triangles:

    Simple triangle to manipulate

    • Choose the Point Tool from the menu on the left of the sketch area.
    • Holding down the shift key (to keep all of the points highlighted) Make three points in the sketch area anywhere.
    • Make sure all three points are selected (bold) they should be if you held shift down.
    • Go to the CONSTRUCT Menu and choose Segment.

    Now let's measure the angles.

    • Holding down the shift key choose the three vertexes of the triangle
    • Go to the MEASURE menu and choose angle. Order is important. Measure all three angles.
    • Click and Drag the points around and notice the changes in the angles
    • Go to the MEASURE Menu and choose Calculate. Now choose an angle measure and then + then another angle and so on. What do they add up to? Drag the vertexes around to notice the measurement.

    Right Triangle

    • Choose the Segment tool from the left
    • Hold Down the shift key and draw a straight horizontal segment
    • Select an end point and (hold shift) the segment
    • Select the CONSTRUCT Menu and choose Perpendicular Line
    • Construct a point on the perpendicular line. Select this point and the other segment endpoint and choose CONSTRUCT Segment
    • Select the perpendicular line and choose DISPLAY Hide the line
    • Now construct the final segment and play with this triangle in the same manner as above.

     

    Square:

    • Select the Segment Tool and construct a horizontal segment
    • Select a point on this segment and choose Mark Center under the TRANSFORM Menu
    • Choose the other point and the segment itself and select rotate 90 or -90 (try and see which is best) under the TRANSFORM Menu
    • Repeat until you have three sides then CONSTRUCT a segment between the two remaining end points.
    • Drag the vertexes around and see what happens. Select all the vertexes and select CONSTRUCT Polygon Interior. While it is highlighted (wavy) choose Color from under DISPLAY Menu. Have fun.

     

    Extensions to try:

    Can you make an equilateral triangle?

    Try making squares on each of the sides of the rt triangle you made. What do you notice about the areas?